Computational Methods in Financial Mathematics Course Project

This course project is made up of two parts. Part one is an investigation and implementation of pricing of financial derivatives using numerical methods for the solution of partial differential equations. Part two is an introduction of Monte Carlo methods in financial engineering. The name of course is MA573:Computational Methods in Financial Mathematics, spring 2009, given by Professor Marcel Blais

Multi-dimensional Channel Parameter Estimation for mmWave Cylindrical Arrays

University of Technology Sydney. Faculty of Engineering and Information Technology.Millimeter-wave (mmWave) large-scale antenna arrays, standardized for the fifth-generation (5G) communication networks, have the potential to estimate channel parameters with unprecedented accuracy, due to their high temporal resolution and excellent directivity. However, most existing techniques have very high complexities in hardware and software, and they cannot effectively exploit the properties of mmWave large-array systems for channel estimation. As a result, their application in 5G mmWave large array systems is limited in practice. This thesis develops new and efficient solutions to channel parameter estimation using large-scale mmWave uniform cylindrical arrays (UCyAs). The key contributions of this thesis are on the following four aspects: We first present a channel compression-based channel estimation method, which reduces the computational complexity substantially at a negligible cost of estimation accuracy. By capitalizing on the sparsity of mmWave channel, the method effectively filters out the useless signal components. As a result, the dimension of the element space of the received signals can be reduced. Next, we extend the channel estimation to the hybrid UCyA case, and design new hybrid beamformers. By exploiting the convergence property of the Bessel function, the designed beamformers can preserve the recurrence relationship of the received signals with a small number of radio frequency (RF) chains. We then arrange the received signals in a tensor form and propose a new tensor-based channel estimation algorithm. By suppressing the receiver noises in all dimensions (time, frequency, and space), the algorithm can achieve substantially higher estimation accuracy than existing matrix-based techniques. Finally, to reduce cost and power consumption while maintaining a high network access capability, we develop a novel nested hybrid UCyA and present the corresponding parameter estimation algorithm based on the second-order channel statistics. Simulation results show that by exploiting the sparse array technique to design the RF chain connection network, the angles of a large number of devices can be accurately estimated with much fewer RF chains than antennas. Overall, this thesis presents several applicable UCyA design schemes and proposes the efficient channel parameter estimation algorithms. The presented new UCyAs can significantly reduce the hardware cost of the system with a marginal accuracy loss, and the proposed algorithms are capable of accurately estimating the channel parameters with low computational complexities. By employing the presented UCyAs and implementing the proposed novel algorithms cohesively, the different communication and deployment requirements of a variety of mmWave communication scenarios can be met

A stable gene selection in microarray data analysis

BACKGROUND: Microarray data analysis is notorious for involving a huge number of genes compared to a relatively small number of samples. Gene selection is to detect the most significantly differentially expressed genes under different conditions, and it has been a central research focus. In general, a better gene selection method can improve the performance of classification significantly. One of the difficulties in gene selection is that the numbers of samples under different conditions vary a lot. RESULTS: Two novel gene selection methods are proposed in this paper, which are not affected by the unbalanced sample class sizes and do not assume any explicit statistical model on the gene expression values. They were evaluated on eight publicly available microarray datasets, using leave-one-out cross-validation and 5-fold cross-validation. The performance is measured by the classification accuracies using the top ranked genes based on the training datasets. CONCLUSION: The experimental results showed that the proposed gene selection methods are efficient, effective, and robust in identifying differentially expressed genes. Adopting the existing SVM-based and KNN-based classifiers, the selected genes by our proposed methods in general give more accurate classification results, typically when the sample class sizes in the training dataset are unbalanced

Distributed and Asynchronous Data Collection in Cognitive Radio Networks with Fairness Consideration

As a promising communication paradigm, Cognitive Radio Networks (CRNs) have paved a road for Secondary Users (SUs) to opportunistically exploit unused licensed spectrum without causing unacceptable interference to Primary Users (PUs). In this paper, we study the distributed data collection problem for asynchronous CRNs, which has not been addressed before. We study the Proper Carrier-sensing Range (PCR) for SUs. By working with this PCR, an SU can successfully conduct data transmission without disturbing the activities of PUs and other SUs. Subsequently, based on the PCR, we propose an Asynchronous Distributed Data Collection (ADDC) algorithm with fairness consideration for CRNs. ADDC collects a snapshot of data to the base station in a distributed manner without the time synchronization requirement. The algorithm is scalable and more practical compared with centralized and synchronized algorithms. Through comprehensive theoretical analysis, we show that ADDC is order-optimal in terms of delay and capacity, as long as an SU has a positive probability to access the spectrum. Furthermore, we extend ADDC to deal with the continuous data collection issue, and analyze the delay and capacity performances of ADDC for continuous data collection, which are also proven to be order-optimal. Finally, extensive simulation results indicate that ADDC can effectively accomplish a data collection task and significantly reduce data collection delay. [ABSTRACT FROM PUBLISHER